16 June 2021

Networks are everywhere.. but what are they?

  • We live in a ‘networked world’

  • The word ‘network’ is ubiquitous:

    • Communication networks
    • Transport networks
    • Social networks
  • Has a formal meaning in mathematics, social and physical sciences: a representation of the relations between entities







Goals of this lecture

  • The lecture will be a brief overview of the origins and concept of network analysis as it applies to humanities subjects.
  • By the end you should:
    • Have a basic knowledge of network analysis and its key concepts
    • Understand key terminology such as nodes and edges
    • Understand some important network measurements and how to interpret them
    • Have a practical starting-point for the tools and methods needed to turn your own research into network data

Leonard Euler, graph theory, and the ‘Königsberg Bridge Problem’

  • Network analysis has its origins in ‘graph theory’, put forward by the 18th-century mathematician Leonhard Euler.
  • Trying to solve the ‘Königsberg Bridge problem’

From Graphs to Networks…

  • Graphs can be used to represent networks of ‘things’ (called nodes) and connections between them (called links or edges).
  • Often represented as a ’network diagram, where the nodes are points and the edges lines.
  • They have a few additional properties: they can be directed and weighted

Directed Networks

  • Directed networks are ones in which the information flows in a particular direction, from one node to another.

Weighted Networks

  • A weighted network is one where these is a measurement representing the strength of the ties between the nodes.

Bipartite Networks

  • Nodes can be of more than one type, for example a network of actors connected to movie genres
  • Known as bipartite or bimodal if there are two types
  • Need additional steps to be analysed in the same way as ‘regular’ networks

Social Network Analysis

  • Graph theory applied to systems of relations between people
  • Eg. Mark Granvetter, ‘Strength of Weak ties’ (1973)
  • Do we learn more from our distant acquaintences than our close friends?

Degree

  • Counts the number of connections to a particular node
  • Can be directed and weighted

Directed Degree

Weighted Degree

Betweenness centrality

  • First an algorithm calculates all the ‘shortest paths’ from every pair of nodes.
  • A node scores highly for betweenness centrality if it is used on many of these paths

Eigenvector centrality

  • Measures importance through a node’s connection to other important nodes
  • Similar to the ‘PageRank’ system used by Google to rank search results by importance.

The "New Science of Networks’

  • Using network theory to understand and map very large complex systems such as the internet
  • Papers by Barabasi (1999) and Watts & Strogatz (1998) shows that many real-world networks have a similar structure
  • A small number of nodes with many connections, often called ‘hubs’, and many nodes with very few connections.

A ‘Small-world’

  • Hubs make it easy to reach other parts of network even with a very few total connections
  • This has been called the ‘small-world’ phenomenon, and helps to explain why everyone is so well-connected to everyone else!
  • These types of networks are also resistant to failure but susceptible to targeted attack.

Network Analysis and the Humanities

  • Networks particularly suitable to humanities data, because we are in the business of relations
  • In the past 20 years has been used to analyse historical social networks, archaeology, geographic networks, historical infrastructure, and others
  • Also relevant to many other areas: even literary studies, art history etc.

Almost anything can be a network..

Networks of cities..

  • In my own research I made a ‘social network of cities’ based on news transmission
  • Network data was collected from printed news sources
  • Needed extensive correction and manual cleaning

Constructing and Analysing Network Data: practical steps

  • Networks very commonly constructed from an ‘edge list’: a list of connections between pairs of nodes, often in a simple spreadsheet with two columns
  • Data can be entered manually on a small scale
  • Lots of existing humanities datasets available online, ready for network analysis.
  • A huge range of software out there to visualise and analyse, for all levels of expertise.

Network Visualisation

  • Often represented as a force-directed network
  • Highly-connected groups of nodes are placed closely together
  • Useful to get a sense of the overall ‘topology’, or map of a network, findings its centres, peripheries and separate clusters

Network Analysis Metrics

  • The metrics above can be used to highlight important nodes
  • Think about the implications of each one for your own data and research
  • For example high degree score in historical social network might indicate an important communicator; high degree in an archaeological network something else entirely.

Pitfalls of Network Analysis

  • Be careful in interpreting the results - particularly with messy data
  • How might your data ‘cleaning’ impact your findings?
  • To what extent are findings the result of collection or archival practices?
  • Some network types (such as bipartite) need additional steps before they can be analysed correctly

Conclusions

  • Networks can be a powerful way to quantitatively assess related objects
  • Easy to analyse with a variety tools
  • Both visualisation and network metrics can be useful
  • Think about how your own data might be represented as a network